What is the best way to increase accuracy of such servo motor ?
Instead, look for inexpensive small bipolar stepper motors with a small angle per step, or invest in microstepping drivers.
A couple of these coupled to an Arduino GRBL CAD shield (cheap as well), with appropriate drivers, would be much more accurate. Use rigid aluminum extrusion for the arms, and only use a servo on the end to lift and place the pen on the paper.
At a certain point in complexity (and cost) you could go with a cartesian plotting system run with the same board, too.
If you don't want open-ended stepper control, adding on an encoder to the stepper isn't too difficult (probably the easiest and cheapest and long-lasting would be to get hall-effect encoder breakout boards and dual-shaft steppers, and mount the boards on brackets to the opposite end of the stepper, and mount the magnet on the shaft with a drop of super glue or epoxy).
You can do all of this easily for well under $100 USD.
Personally I like the fact that it's somewhat sloppy. The pictures have a distinct style.
Timing: assuming rigidity of linear position is crappy, allow more time for it to bounce back.
Speed: ramp-up speed in one direction may be different from the opposite direction.
Position: accuracy of RC servos is almost not worth measuring, so many companies haven't. But you can hack it (via contact switch and something that juts out) to add a simple shaft rotation encoding and correct when needed.
Software correction: draw a grid of straight lines and adjust drift in software until it looks like a grid.